Does the volitional form of a verb mean both "let's" and "I want to"?

Question

I was taught ages ago that the volitional form of a verb means "let's" do something. For example, if you take `行{い}く` and change it to `行{い}こう`, you get "let's go". However, I feel like I can use the same form to express "I want to". For example: > 行{い}こうかなと思{おも}っている ("[I'm] thinking maybe I'll go") Am I wrong that it can be used this way? If it's true that it can mean that, what is the difference between the sentence I have above and this one: > 行{い}くかなと思{おも}っている My understandng of the plain form is that it can be used to imply future tense, and if so, maybe it also implies intention. If so, then the two sentences mean the same thing, don't they? Perhaps I'm thinking too much in English, though, where "will go" can be both intention and future tense? So, my questions in summary are: Does `行{い}こう` mean "will go" as well as "let's go"? Can `行{い}こう` and `行{い}く` both be used to mean future tense and/or intention?

Answer 1

The volitional can certainly be used as a "Let's~" statement, as well as express one's own intention to do something.

行こうかなと思っている - I'm wondering if I'll go/it would be nice to go. Kind of wishy-washy; you haven't made up your mind yet.

行くかなと思っている - I'm wondering if (she'll) go. She's expressed interest or indecision.

行こうと思っている - I'm thinking that I'll go. I'm pretty firm on my decision to go. 50%> serious.

The volitional can be used to volunteer one's services too:

何かを手伝いましょうか。Can I help you with anything?